Difference between Permutations and Combinations

What is the main difference between permutations and combinations?

The main difference between permutations and combinations is that permutations consider the order of elements, whereas combinations do not. In permutations, the arrangement of elements matters, while in combinations, it does not.

When should you use permutations instead of combinations?

You should use permutations when the order of elements is important, such as in arranging books on a shelf or determining the sequence of tasks. Use combinations when the order does not matter, such as selecting a team from a group of people.

How do you calculate permutations?

Permutations are calculated using the formula ​, where nnn is the total number of items, and r is the number of items to arrange. The symbol !!! denotes factorial, which is the product of all positive integers up to that number.

How do you calculate combinations?

Combinations are calculated using the formula C(n,r)=n!r!(n−r)!C(n, r) = \frac{n!}{r!(n-r)!}C(n,r)=r!(n−r)!n!​, where nnn is the total number of items, and rrr is the number of items to select. The formula accounts for the fact that the order of selection does not matter.

Difference between Permutations and Combinations: Probability is concerned with the chance or possibility that an event may occur or not occur if there are ‘n’ possibilities. Put simply, probability tells us the percentage of happening of an event. Probability can be expressed as a number from 0 to 1 or as a percentage. 

In this article, we will discuss the difference between Permutations and Combinations, with their definition, and formulas.